Communication techniques involving pairwise orthogonality of adjacent rows in LPDC code

Abstract

Certain aspects of the present disclosure provide low-density parity-check (LDPC) codes having pairwise orthogonality of adjacent rows, and a new decoder that exploits the pairwise row orthogonality for flexible decoder scheduling without performance loss. An apparatus includes a receiver configured to receive a codeword in accordance with a radio technology across a wireless channel via one or more antenna elements situated proximal the receiver. The apparatus includes at least one processor coupled with a memory and comprising decoder circuitry configured to decode the codeword based on a LDPC code to produce a set of information bits. The LDPC code is stored in the memory and defined by a base matrix having columns in which all adjacent rows are orthogonal in a last portion of the rows.

What is claimed is: 
     
       1. An apparatus for wireless communication, comprising:
 a receiver configured to receive a codeword in accordance with a radio technology across a wireless channel via one or more antenna elements situated proximal the receiver; and 
 at least one processor coupled with a memory and comprising decoder circuitry configured to decode the codeword based on a low density parity check (LDPC) code to produce a set of information bits, wherein: 
 the LDPC code is stored in the memory and defined by a base matrix having a first number plurality of columns corresponding to variable nodes of a base graph and a second number plurality of rows corresponding to check nodes of the base graph, and; 
 elements in all adjacent rows of a column are orthogonal, for each of the first number plurality of columns, all adjacent rows are orthogonal in a last portion of the second number of at least twenty-one rows starting from a last row of the base matrix; and 
 each row of the twenty-one rows contains a non-zero element in a first column, of the plurality of columns, with a column index 0, or a non-zero element in a second column, of the plurality of columns, with a column index 1. 
 
     
     
       2. The apparatus of  claim 1 , wherein entries each element in the base matrix correspond corresponds to an edge between the a variable node and the a check node, of the a base graph, associated with the entry in base matrix. 
     
     
       3. The apparatus of  claim 2 , wherein entries each non-zero element in the base matrix include corresponds to a cyclic integer lifting values value. 
     
     
       4. The apparatus of  claim 2 , wherein in each column of the first number plurality of columns, at most one row of each pair of the adjacent orthogonal rows in the last portion of the twenty-one rows has an entry contains a non-zero element. 
     
     
       5. The apparatus of  claim 1 , wherein the last portion of the rows comprises at least the bottom twenty-one rows of the base matrix.  
     
     
       6. The apparatus of  claim 1 , wherein the memory is configured to store at least a portion of the LDPC code. 
     
     
       7. The apparatus of  claim 1 , wherein the at least one processor includes a layered decoder configured to decode the codeword. 
     
     
       8. The apparatus of  claim 1 , wherein the at least one processor is configured to decode the codeword based on a decoding schedule. 
     
     
       9. The apparatus of  claim 8 , wherein the decoding schedule includes decoding at least one processor is configured to decode the codeword based on the LDPC code by decoding sequentially row by row in the base matrix or by to simultaneously decoding decode pairs of rows in the base matrix based on the decoding schedule. 
     
     
       10. The apparatus of  claim 9 , wherein the at least one processor is configured to select from two combinations a combination of two rows from any three sequential rows in the last portion for the simultaneous decoding pairs of the decoding schedule twenty-one rows to simultaneously decode. 
     
     
       11. The apparatus of  claim 9 , wherein the row by row or pairs of rows is performed at least one processor is further configured to decode sequentially column by column in the base matrix. 
     
     
       12. The apparatus of  claim 8 , wherein the decoding schedule includes skipping at least one processor is further configured to skip decoding portions elements of the base matrix that do not contain an associated entry a zero. 
     
     
       13. The apparatus of  claim 1 , wherein the LDPC code comprises a lifted LDPC code. 
     
     
       14. The apparatus of  claim 1 , wherein:
 the codeword comprises a punctured codeword,; and  
 the at least one processor further comprises a depuncturer configured to depuncture the codeword, and 
 the decoding comprises decoding the depunctured codeword. 
 
     
     
       15. An apparatus for wireless communication, comprising:
 at least one processor coupled with a memory and comprising an encoder circuit configured to encode a set of information bits based on a low density parity check (LDPC) code to produce a codeword, wherein:
 the LDPC code is stored in the memory and defined by a base matrix having a first number plurality of columns corresponding to variable nodes of a base graph and a second number plurality of rows corresponding to check nodes of the base graph, and; 
 elements in all adjacent rows of a column are orthogonal, for each of the first number plurality of columns, all adjacent rows are orthogonal in a last portion of the second number of at least rows starting from a last row of the base matrix; and 
 each row of the twenty-one rows contains a non-zero element in a first column, of the plurality of columns, with a column index 0, or a non-zero element in a second column, of the plurality of columns, with a column index 1; and 
 
 a transmitter configured to transmit the codeword in accordance with a radio technology across a wireless channel via one or more antenna elements arranged proximal the transmitter. 
 
     
     
       16. The apparatus of  claim 15 , wherein entries each element in the base matrix correspond corresponds to an edge between the a variable node and the a check node, of the a base graph, associated with the entry in base matrix. 
     
     
       17. The apparatus of  claim 16 , wherein entries each non-zero element in the base matrix are replaced corresponds to a cyclic integer lifting values value. 
     
     
       18. The apparatus of  claim 16 , wherein in each column of the first number plurality of columns, at most one row of each pair of the adjacent orthogonal rows in the last portion of the twenty-one rows has an entry contains a non-zero element. 
     
     
       19. The apparatus of  claim 15 , wherein the last portion of the rows comprises at least the bottom twenty-one rows of the base matrix. 
     
     
       20. The apparatus of  claim 15 , wherein:
 the at least one processor is further configured to lifted the LDPC code by generating generate an integer number of copies of the base matrix; and 
 the LDPC code comprises a lifted LDPC code to lift the LDPC code. 
 
     
     
       21. The apparatus of  claim 15 , wherein:
 the at least one processor further comprises a puncturer configured to puncture the codeword, and 
 the transmitting the codeword comprises transmitting transmitter is configured to transmit the punctured codeword. 
 
     
     
       22. A method for wireless communication, comprising:
 receiving a codeword in accordance with a radio technology across a wireless channel via one or more antenna elements situated proximal a receiver; and 
 decoding the codeword via decoder circuitry based on a low density parity check (LDPC) code to produce a set of information bits, wherein:
 the LDPC code is stored in a memory and defined by a base matrix having a first number plurality of columns corresponding to variable nodes of a base graph and a second number plurality of rows corresponding to check nodes of the base graph, and;  
 elements in all adjacent rows of a column are orthogonal, for each of the first numberplurality of columns, all adjacent rows are orthogonal in a last portion of the second number of at least twenty-one rows starting from a last row of the base matrix; and 
 each row of the twenty-one rows contains a non-zero element in a first column, of the plurality of columns, with a column index 0, or a non-zero element in a second column, of the plurality of columns, with a column index 1. 
 
 
     
     
       23. The method of  claim 22 , wherein in each column of the first number plurality of columns, at most one row of each pair of the adjacent orthogonal rows in the last portion of the twenty-one rows has an entry a non-zero element. 
     
     
       24. The method of  claim 22 , wherein the last portion of the rows comprises at least the bottom twenty-one rows of the base matrix. 
     
     
       25. The method of  claim 22 , wherein: the decoding is based on a decoding schedule; and the decoding schedule the codeword includes decoding the codeword based on the LDPC code by decoding sequentially row by row in the base matrix or by simultaneously decoding pairs of rows in the base matrix based on a decoding schedule. 
     
     
       26. The method of  claim 25 , further comprising selecting from two combinations of two each pair of the pairs of rows from any three sequential rows in of the last portion for the simultaneous decoding pairs of the decoding schedule twenty-one rows to decode. 
     
     
       27. A method for wireless communication, comprising:
 encoding a set of information bits with encoder circuitry based on a low density parity check (LDPC) code to produce a codeword wherein:
 the LDPC code is stored in a memory and defined by a base matrix having a first number plurality of columns corresponding to variable nodes of a base graph and a second number plurality of rows corresponding to check nodes of the base graph, and; 
 elements in all adjacent rows of a column are orthogonal, for each of the first number plurality of columns, all adjacent rows are orthogonal in a last portion of the second number of at least twenty-one rows starting from a last row of the base matrix; and 
 each row of the twenty-one rows contains a non-zero element in a first column, of the plurality of columns, with a column index 0, or a non-zero element in a second column, of the plurality of columns, with a column index 1; and 
 
 transmitting the codeword in accordance with a radio technology across a wireless channel via one or more antenna elements. 
 
     
     
       28. The method of  claim 27 , wherein in each column of the first number plurality of columns, at most one row of each pair of the adjacent orthogonal rows in the last portion of the twenty-one rows has an entry contains a non-zero element. 
     
     
       29. The method of  claim 27 , wherein the last portion of the rows comprises at least the bottom twenty-one rows of the base matrix. 
     
     
       30. The method of  claim 27 , further comprising puncturing the codeword, wherein transmitting the codeword comprises transmitting the punctured codeword. 
     
     
       31. The apparatus of claim 1, wherein each row of the plurality of rows, except the twenty-one rows, contains a non-zero element in the first column, a non-zero element in the second column, or a non-zero element in both the first column and the second column. 
     
     
       32. The apparatus of claim 1, wherein:
 the set of information bits is K information bits, where K is a positive integer;   the base matrix is a base matrix H lifted by a lifting factor Z;   the plurality of columns consists of V columns corresponding to i variable nodes, where V is 68;   the plurality of rows consists of C rows corresponding to j check nodes, where C is 46; and   the elements in the base matrix are represented by a row index i and a column index j.   
     
     
       33. The apparatus of claim 32, wherein an element V i,j  of the base matrix is a non-zero element at least when i=[25], j=[1]; i=[26], j=[0]; i=[27], j=[1]; i=[28], j=[0]; i=[29], j=[1]; i=[30], j=[0]; i=[31], j=[1]; i=[32], j=[0]; i=[33], j=[1]; i=[34], j=[0]; i=[35], j=[1]; i=[36], j=[0]; i=[37], j=[1]; i=[38], j=[0]; i=[39], j=[1]; i=[40], j=[0]; i=[41], j=[1]; i=[42], j=[0]; i=[43], j=[1]; i=[44], j=[0]; i=[45], j=[1]. 
     
     
       34. The apparatus of claim 33, wherein an element V i,j  of the base matrix is further a non-zero element at least when j=[0] and i=[24], i=[22], i=[20], i=[19], i=[17], i=[15], i=[14], i=[13], i=[12], i=[11], i=[9], i=[8], i=[7], i=[6], i=[5], i=[4], i=[3], i=[2], i=[1], i=[0]; and when j=[1] and i=[23], i=[21], i=[20], i=[19], i=[18], i=[16], i=[15], i=[12], i=[11], i=[10], i=[9], i=[8], i=[7], i=[5], i=[4], i=[3], i=[2], i=[0]. 
     
     
       35. The apparatus of claim 1, wherein:
 the receiver is configured to receive the codeword in accordance with a radio technology across a wireless channel via one or more antenna elements situated proximal the receiver;   the at least one processor is configured to select a combination pairs of rows from any three sequential rows in the twenty-one rows; and   the at least one processor comprises decoder circuitry configured to simultaneously decode each pair of rows.   
     
     
       36. The apparatus of claim 1, wherein the first column having the column index 0 and the second column having the column index 1 have a highest degree among the plurality of columns, where the first column and the second column have a highest number of non-zero entries among the plurality of columns. 
     
     
       37. The apparatus of claim 36, wherein:
 the codeword comprises a punctured codeword, where systematic bits corresponding to the first column and the second column are punctured; and   the at least one processor comprises a depuncturer configured to depuncture the systematic bits corresponding to the first column and the second column.   
     
     
       38. The apparatus of claim 15, wherein each row of the plurality of rows, except the twenty-one rows, contains a non-zero element in the first column, a non-zero element in the second column, or a non-zero element in both the first column and the second column. 
     
     
       39. The apparatus of claim 15, wherein:
 the set of information bits is K information bits, where K is a positive integer;   the base matrix is a base matrix H lifted by a lifting factor Z;   the plurality of columns consists of V columns corresponding to i variable nodes, where V is 68;   the plurality of rows consists of C rows corresponding to j check nodes, where C is 46; and   the elements in the base matrix are represented by a row index i and a column index j.   
     
     
       40. The apparatus of claim 39, wherein an element V i,j  of the base matrix is a non-zero element at least when i=[25], j=[1]; i=[26], j=[0]; i=[27], j=[1]; i=[28], j=[0]; i=[29], j=[1]; i=[30], j=[0]; i=[31], j=[1]; i=[32], j=[0]; i=[33], j=[1]; i=[34], j=[0]; i=[35], j=[1]; i=[36], j=[0]; i=[37], j=[1]; i=[38], j=[0]; i=[39], j=[1]; i=[40], j=[0]; i=[41], j=[1]; i=[42], j=[0]; i=[43], j=[1]; i=[44], j=[0]; i=[45], j=[1]. 
     
     
       41. The apparatus of claim 40, wherein an element V i,j  of the base matrix is further a non-zero element at least when j=[0] and i=[24], i=[22], i=[20], i=[19], i=[17], i=[15], i=[14], i=[13], i=[12], i=[11], i=[9], i=[8], i=[7], i=[6], i=[5], i=[4], i=[3], i=[2], i=[1], i=[0]; and when j=[1] and i=[23], i=[21], i=[20], i=[19], i=[18], i=[16], i=[15], i=[12], i=[11], i=[10], i=[9], i=[8], i=[7], i=[5], i=[4], i=[3], i=[2], i=[0]. 
     
     
       42. The apparatus of claim 15, wherein:
 the transmitter is configured to transmit the codeword in accordance with a radio technology across a wireless channel via one or more antenna elements situated proximal the transmitter;   the at least one processor is configured to select a combination pairs of rows from any three sequential rows in the twenty-one rows; and   the at least one processor comprises encoder circuitry configured to simultaneously encode each pair of rows.   
     
     
       43. The apparatus of claim 15, wherein the first column having the column index 0 and the second column having the column index 1 have a highest degree among the plurality of columns, where the first column and the second column have a highest number of non-zero entries among the plurality of columns. 
     
     
       44. The apparatus of claim 43, wherein the at least one processor comprises a puncturer configured to puncture systematic bits in the codeword corresponding to the first column and the second column. 
     
     
       45. The apparatus of claim 1, wherein the receiver is configured to receive the codeword in accordance with a radio technology across a wireless channel via one or more antenna elements situated proximal the receiver. 
     
     
       46. The apparatus of claim 15, wherein the transmitter is configured to transmit the codeword in accordance with a radio technology across a wireless channel via one or more antenna elements situated proximal the transmitter.